Practice Quiz #3
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Consider the function f(x)=xm(1−x)n on the segment [0;1]. Find the coordinate of its maximum; if it does not exists, write −1000.
Find the convexity (or the concavity) of the function f(x)=x3−1x4 for x>1. Write "CONVEX" or "CONCAVE" respectively.
Consider the function f(x)=xx. Find its local extremum (there is only one); write its coordinate and the type ("MAXIMUM" or "MINIMUM", separate with semi-colon ).